We consider the effects of parallelizing branch-and-bound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branch-and-bound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermore, it is also possible to achieve speedups that are in excess of the ratio n 2 /n 1 . Experimental results with the 0/1-Knapsack and Traveling Salesperson problems are also presented.

In this paper we develop parallel A* algorithms suitable for distributed-memory machines. In parallel A* algorithms, inefficiencies grow with the number of processors P used, causing performance to drop significantly at lower and intermediate work densities (the ratio of the problem size to P ). To alleviate this effect, we propose a novel parallel startup phase and efficient dynamic work distribution strategies, and thus improve the scalability of parallel A* search. We also tackle the problem of duplicate searching by different processors, by using work transfer as a means to partial duplicate pruning. The parallel startup scheme proposed requires only \Theta(logP ) time compared to \Theta(P ) time for sequential startup methods used in the past. Using the Traveling Salesman Problem (TSP) as our test case, we see that our work distribution strategies yield speedup improvements of more than 30% and 15% at lower and intermediate work densities, respectively, while requiring 20% to 45%...

The goal of this research is to develop a systematic, integrated method of designing efficient search algorithms that solve optimization problems in real time. Search algorithms studied in this thesis comprise meta-control and primitive search. The class of optimization problems addressed are called combinatorial optimization problems, examples of which include many NP-hard scheduling and planning problems, and problems in operations research and artificial-intelligence applications. The problems we have addressed have a well-defined problem objective and a finite set of well-defined problem constraints. In this research, we use state-space trees as problem representations. The approach we have undertaken in designing efficient search algorithms is an engineering approach and consists of two phases: (a) designing generic search algorithms, and (b) improving by genetics-based machine learning methods parametric heuristics used in the search algorithms designed. Our approach is a systematic method that integrates domain knowledge, search techniques, and automated learning techniques for designing better search algorithms. Knowledge captured in designing one search algorithm can be carried over for designing new ones. iv ACKNOWLEDGEMENTS I express my sincere gratitude to all the people who have helped me in the course of my graduate study. My thesis advisor, Professor Benjamin W. Wah, was always available for discussions and encouraged me to explore new ideas. I am deeply grateful to the committee

For many applications of the A* algorithm, the state space is a graph rather than a tree. The implication of this for parallel A* algorithms is that different processors may perform significant duplicated work if interprocessor duplicates are not pruned. In this paper, we consider the problem of duplicate pruning in parallel A* graph-search algorithms implemented on distributed-memory machines. A commonly used method for duplicate pruning uses a hash function to associate with each distinct node of the search space a particular processor to which duplicate nodes arising in different processors are transmitted and thereby pruned. This approach has two major drawbacks. First, load balance is determined solely by the hash function. Second, node transmissions for duplicate pruning are global; this can lead to hot spots and slower message delivery. To overcome these problems, we propose two different duplicate pruning strategies: (1) To achieve good load balance, we decouple the task of dup...

In parallel A* graph search on distributed-memory machines, different processors may perform significant duplicated work if inter-processor duplicates are not pruned. The only known method for duplicate pruning associates a particular processor with each distinct node of the search space using a suitable hash function. Then duplicate nodes arising in different processors are transmitted to the same processor, and thereby pruned. There are two main drawbacks attributable to such an approach: (1) Load balance is determined solely by the hash function and is unsatisfactory. (2) Node transmissions for duplicate pruning are global; this can lead to hot spots in the network. We propose two different duplicate pruning techniques that outperform this hashing-only method by using: (1) separate algorithms for duplicate pruning and load balancing, and (2) a novel search space partitioning scheme that evenly spreads out the bandwidth requirement for pruning over the entire parallel architecture. U...